2x^2+3x+5=x^2+6x+9

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Solution for 2x^2+3x+5=x^2+6x+9 equation:


Simplifying
2x2 + 3x + 5 = x2 + 6x + 9

Reorder the terms:
5 + 3x + 2x2 = x2 + 6x + 9

Reorder the terms:
5 + 3x + 2x2 = 9 + 6x + x2

Solving
5 + 3x + 2x2 = 9 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
5 + -9 + 3x + -6x + 2x2 + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: 5 + -9 = -4
-4 + 3x + -6x + 2x2 + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: 3x + -6x = -3x
-4 + -3x + 2x2 + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-4 + -3x + 1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Reorder the terms:
-4 + -3x + 1x2 = 9 + -9 + 6x + -6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-4 + -3x + 1x2 = 0 + 6x + -6x + x2 + -1x2
-4 + -3x + 1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-4 + -3x + 1x2 = 0 + x2 + -1x2
-4 + -3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + -3x + 1x2 = 0

Factor a trinomial.
(-1 + -1x)(4 + -1x) = 0

Subproblem 1

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-1, 4}

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